How do you solve

Question

-2x + y + 4z = 5
X + 3y - z = 2
4x + y -6 z =11

Answer 1

From the second equation, x = 2-3y+z

 

Replace x by 2-3y+z in the other two equations to get:

 

-2(2-3y+z)+y+4z=5

 4(2-3y+z)+y-6z = 11

 

Simplifying, we have:  7y+2z = 9

                             -11y-2z  = 3

 

Adding the equations gives -4y = 12    So, y = -3

 

Since y = -3 and 7y+2z=9, we obtain -21+2z=9

 

                                                           2z=30

            

                                                             z = 15

 

Since y=-3, z=15 and x=2-3y+z, x = 2+9+15 = 26

 

Solution:  x = 26, y = -3, z = 15

 

                       

 

   

Answer 2

Are you familiar with Cramer's rule for solving a system of n linear equations in n unknowns?

Find the determinant of the coefficient matrix. Call it D.

Find the determinants D_x, D_y, and D_z of the 3 matrices:

For D_x replace the first column of the coefficient matrix with the column of constants on the right.

For D_y replace the second column of the coefficient matrix with the column of constants on the right.

For D_z replace the third column of the coefficient matrix with the column of constants on the right.

Then x = D_x/D, y = D_y/D, z = D_z/D

Note that if D = 0, there is no solution.

Answer 3

You work with two equations at a time, trying to eliminate

one of the variables

 

working with equations 1 and 2 you

could easily eliminate the x in #1

 

Then working with equations 2 and 3 you could

easily eliminate the x in #3

 

Now you would have two equations with only two unknowns: y and z

 

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